Generates an SVG Sierpinski triangle in ELM, demo: http://codepen.io/gvangool/full/vGGzjb/

sierpinski-triangle-svg.elm

import Svg exposing (Svg, svg, g, use, defs)
import Svg.Attributes exposing (..)
import Html

triangle_path = "M0 0,2 0,1 1.732 z"
matrix1 = "matrix(0.5 0 0 0.5 0   0)"
matrix2 = "matrix(0.5 0 0 0.5 1   0)"
matrix3 = "matrix(0.5 0 0 0.5 0.5 0.866)"

getLevels : Int -> List (Svg n)
getLevels n =
  case n of
    0 ->
      [Svg.path [id "lev0", fill "#039", d triangle_path] []]
    _ ->
      let
        levp = "#lev" ++ toString (n - 1)
        levn = "lev" ++ toString n
      in
        getLevels (n - 1) ++ [g [id levn]
                  [ use [xlinkHref levp, transform matrix1] []
                  , use [xlinkHref levp, transform matrix2] []
                  , use [xlinkHref levp, transform matrix3] []
                  ]]


main =
  svg [ version "1.1", x "0", y "0", width "600", height "400" ]
    [ defs [] (getLevels 5)
    , use [xlinkHref "#lev5", transform "translate(50,50) scale(200)"] []
    ]